Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Can you picture how to order the cards to reproduce Charlie's card trick for yourself?

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Imagine a very strange bank account where you are only allowed to do two things...

Play this game to learn about adding and subtracting positive and negative numbers

Try out some calculations. Are you surprised by the results?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Take a look at the video showing rhombuses and their diagonals...

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

Take a look at the video showing areas of different shapes on dotty grids...

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

What do you think is going to happen in this video clip? Are you surprised?

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

How many moves does it take to swap over some red and blue frogs? Do you have a method?

Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

Watch this animation. What do you see? Can you explain why this happens?

Dotty Six is a simple dice game that you can adapt in many ways.

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Here is a chance to create some Celtic knots and explore the mathematics behind them.

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Newspapers said that eating a bacon sandwich every day raises the risk of bowel cancer by 20%. Should you be concerned?

Video showing how to use the Number Plumber

Alf and Tracy explain how the Kingsfield School maths department use common tasks to encourage all students to think mathematically about key areas in the curriculum.

Design and test a paper helicopter. What is the best design?

Video for teachers of a talk given by Dan Meyer in Cambridge in March 2013.

The Enigma Project's James Grime has created a video code challenge. Watch it here!